Multiplicity considerations for subgroup analysis subject to consistency constraint

A significant heterogeneity in response across subgroups of a clinical trial implies that the average response from the overall population might not characterize the treatment effect; and as noted by different regulatory guidances, can cause concerns in interpreting study findings and might lead to restricting treatment labeling. However, along with the challenges raised by the heterogeneity, recently there has been growing interest in taking advantage of the expected variability in response across subgroups to increase the chance of success of a trial by designing the trial with objectives of establishing efficacy claims for the total population and a targeted subgroup. For such trials, there have been several approaches to address the multiplicity issue with the two paths of success. This manuscript advocates the utility of setting a threshold on the treatment effect for the subgroups at the design stage to guide determination of the population labeling when significant findings for the total population have been established. Specifically, it proposes that licensing treatment for the total population requires, in addition to significant findings for this population, that the treatment effect in the least benefited (complementary) subgroup meets the treatment effect threshold at a minimum; otherwise, the treatment would be restricted to the targeted subgroup only. Setting such a threshold can be based on clinical considerations, including toxicity and adverse events, in addition to treatment effect in the subgroup. This manuscript expands some of the multiplicity approaches to account for the threshold requirement and investigates the impact of the threshold requirement on study power.